I have been trying a little braiding at work this week, and here is a solution that seems to work.
I made drawings but they are of such a poor quality that I do not put them on line.
If the written version does not work for you I might make better drawings.
Tie your strings into the knot above the start of the braid, (or tie them together so that they are in the right order),
devide the strings so that you have the one in the middle at the top as most outside in either hand, and the ones in the middle at the bottom next to each other.
Number them 1 to 8 for now, for explanation only.
Cross 5 over 4,
3 over 5 (in between 5 and 4)
6 over 4 and 3, (between 5 and 3)
Start braiding with strand 8, going over the stands, down next to number 2 and back to its own side under the strands.
I hope you understand what I try to say.
I tried it with 4 colours, they started as 1,2,3,4,1,2,3,4, when braiding they were 1,2,1,2,3,4,3,4.
Willeke